Geodesic
On mixed complex intersection bodies
Zhao, Chang-Jian 1
1 Department of Mathematics, China Jiliang University, Hangzhou 310018, P. R. China
Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 4, p. 541-549.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In 2013, the mixed complex intersection bodies of star bodies was introduced. Following this, in the paper, we establish Aleksandrov-Fenchel and Brunn-Minkowski type inequalities for the mixed complex intersection bodies, which in special case yield some of the recent results.
DOI : 10.22436/jnsa.011.04.10
Classification : 52A40
Keywords: Dual Minkowski inequality, Dual Brunn-Minkowski inequality, Width-integrals, Affine surface area, Projection body

Zhao, Chang-Jian  1

1 Department of Mathematics, China Jiliang University, Hangzhou 310018, P. R. China 
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Zhao, Chang-Jian . On mixed complex intersection bodies. Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 4, p. 541-549. doi : 10.22436/jnsa.011.04.10. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.04.10/

[1] Busemann, H. Volume in terms of concurrent cross-sections, Pacific J. Math., Volume 3 (1953), pp. 1-12 | Zbl | DOI

[2] S. Campi Stability estimates for star bodies in terms of their intersection bodies, Mathematika, 45, 287–303., 1998 | Zbl | DOI

[3] S. Campi Convex intersection bodies in three and four dimensions, Mathematika, Volume 46 (1999), pp. 15-27 | DOI

[4] Fallert, H.; Goodey, P.; Weil, W. Spherical projections and centrally symmetric sets, Adv. Math., Volume 129 (1997), pp. 301-322 | DOI

[5] R. J. Gardner A positive answer to the Busemann–Petty problem in three dimensions, Ann. of Math., Volume 140 (1994), pp. 435-447 | DOI | Zbl

[6] Gardner, R. J. Intersection bodies and the Busemann-Petty problem, Trans. Amer. Math. Soc., Volume 342 (1994), pp. 435-445 | DOI

[7] R. J. Gardner On the Busemann-Petty problem concerning central sections of centrally symmetric convex bodies, Bull. Amer. Math. Soc., Volume 30 (1994), pp. 222-226 | Zbl

[8] Gardner, R. J. Geometric Tomography, Cambridge University Press, Volume Cambridge (1995)

[9] R. J. Gardner The Brunn-Minkowski inequality, Bull. Amer. Math. Soc., Volume 39 (2002), pp. 355-405 | DOI

[10] Gardner, R. J.; Koldobsky, A.; Schlumprecht, T. An analytic solution to the Busemann-Petty problem , C. R. Acad. Sci. Paris Sér. I Math., Volume 328 (1999), pp. 29-34 | DOI

[11] Gardner, R. J.; Koldobsky, A.; Schlumprecht, T. An analytic solution to the Busemann-Petty problem on sections of convex bodies, Ann. of Math., Volume 149 (1999), pp. 691-703 | DOI | Zbl

[12] Goodey, P.; Lutwak, E.; Weil, W. Functional analytic characterizations of classes of convex bodies, Math. Z., Volume 222 (1996), pp. 363-381 | DOI | Zbl

[13] Goodey, P.; Weil, W. Intersection bodies and ellipsoids, Mathematika, Volume 42 (1995), pp. 295-304 | DOI

[14] Grinberg, E.; Zhang, G. Convolutions, transforms, and convex bodies, Proc. London Math. Soc., Volume 78 (1999), pp. 77-115 | DOI

[15] Koldobsky, A. Intersection bodies, positive definite distributions, and the Busemann-Petty problem, Amer. J. Math., Volume 120 (1998), pp. 827-840 | DOI | Zbl

[16] A. Koldobsky Intersection bodies in \(R^4\) , Adv. Math., Volume 136 (1998), pp. 1-14 | DOI

[17] Koldobsky, A. Second derivative test for intersection bodies, Adv. Math., Volume 136 (1998), pp. 15-25 | Zbl | DOI

[18] A. Koldobsky A functional analytic approach to intersection bodies, Geom. Funct. Anal., Volume 10 (2000), pp. 1507-1526 | DOI | Zbl

[19] A. Koldobsky Fourier Analysis in Convex Geometry, American Mathematical Society, Providence, 2005 | DOI

[20] Koldobsky, A.; Paouris, G.; M. Zymonopoulou Complex Intersection Bodies, J. Lond. Math. Soc., Volume 88 (2013), pp. 538-562 | DOI

[21] Ludwig, M. Intersection bodies and valuations, Amer. J. Math., Volume 128 (2006), pp. 1409-1428 | DOI

[22] E. Lutwak Intersection bodies and dual mixed volumes , Adv. in Math., Volume 71 (1988), pp. 232-261 | DOI

[23] Moszyńska, M. Quotient star bodies, intersection bodies, and star duality, J. Math. Anal. Appl., Volume 232 (1999), pp. 45-60 | DOI | Zbl

[24] Wang, W.; He, R.; Yuan, J. Mixed complex intersection bodies, Math. Inequal. Appl., Volume 18 (2015), pp. 419-428 | DOI

[25] G. Zhang A positive solution to the Busemann-Petty problem in \(R^4\) , Ann. of Math., Volume 149 (1999), pp. 535-543 | DOI

[26] C.-J. Zhao Extremal Problems in Convex Bodies Geometry , Dissertation for the Doctoral Degree at Shanghai Univ., Shanghai, 2005

[27] Zhao, C.-J. \(L_p\)-mixed intersection bodies , Sci. China, Volume 51 (2008), pp. 2172-2188 | DOI

[28] Zhao, C.-J. On intersection and mixed intersection bodies, Geom. Dedicata, Volume 141 (2009), pp. 109-122 | DOI

[29] Zhao, C.-J.; G.-S. Leng Brunn-Minkowski inequality for mixed projection bodies, J. Math. Anal. Appl., Volume 301 (2005), pp. 115-123 | DOI

[30] Zhao, C.-J.; Leng, G.-S. Inequalities for dual quermassintegrals of mixed intersection bodies, Proc. Indian Acad. Sci. Math. Sci., Volume 115 (2005), pp. 79-91 | DOI

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